What are 2 numbers added to get - 17 and if you multiply those same numbers you'll get 72

Any two negative numbers will always give you a positive number, so let's just ignore the - for now.

Straight away, two numbers that multiply to give 72 is 8 and 9. This is just basic multiplying. Now, to check if it adds to 17 (because we're ignoring the minus for now), you just do 8 + 9, which coincidentally happens to be 17. So you just place a minus in front of 8, and a minus in front of 9, and you get - 8 * - 9 = 72, and - 8 + - 9 = - 17.